时滞标准神经网络模型及其应用

Delayed Standard Neural Network Model and Its Application

提出一种新的神经网络模型—时滞标准神经网络模型(DSNNM),它由线性动力学系统和有界静态时滞非线性算子连接而成.利用不同的Lyapunov 泛函和S 方法推导出DSNNM 全局渐近稳定性和全局指数稳定性的充分条件,这些条件可表示为线性矩阵不等式(LMI)形式.大多数时滞(或非时滞)动态神经网络(DANN)稳定性分析或神经网络控制系统都可以转化为DSNNM,以便用统一的方法进行稳定性分析或镇定控制.从DSNNM 应用于时滞联想记忆(BAM)神经网络的稳定性分析以及PH 中和过程神经控制器的综合实例, 可以看出,得到的稳定性判据扩展并改进了以往文献中的稳定性定理,而且可将稳定性分析推广到非线性控制系统的综合.

A novel neural network model, named delayed standard neural network model （DSNNM）, is proposed, which is the interconnection of a linear dynamic system and a bounded static delayed nonlinear operator. By combining a number of different Lyapunov funetionals with S-Procedure, some sufficient conditions for global asymptotic stability and global exponential stability of the DSNNM are derived and formulated as linear matrix inequalities （LMIs）. Most delayed （or non-delayed） dynamic artificial neural networks （DANNs） or neuro-control systems can be transformed into DSNNMs so that stability analysis or stabilization synthesis can be done in a unified way. In this paper, DSNNMs are applied to analyzing the stability of the delayed bidirectional associative memory （BAM） neural networks and synthesizing the neuro-controllers for the PH neutralization process. The stability criteria obtained turn out to be a generalization of some previous criteria. The analysis approach is further extended to the nonlinear control system.